Fractional Legendre transformation

M. A. Alonso*, G. W. Forbes

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    A new transformation is defined that connects a function and its Legendre transform by means of a continuous free parameter. The cyclic behaviour of consecutive Legendre transformations is reflected in the periodic dependence of the new transform on this parameter. This transformation opens new options wherever the conventional Legendre transformation is used (including mechanics, thermodynamics and optics) and is suggestively derived here by considering the geometrical-optics limit of a diffraction integral. The connection to a classical limit of the fractional Fourier transformation is also established and the mathematical and geometrical properties of the transformation are demonstrated.

    Original languageEnglish
    Article number008
    Pages (from-to)5509-5527
    Number of pages19
    JournalJournal of Physics A: Mathematical and General
    Issue number19
    Publication statusPublished - 1995


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